Finite Group Databasebeta

← Group #279402

Character table — Group #279402

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442222444444444444888888884444488888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ5111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11-1
χ6111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-11
χ7111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-11
χ8111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-11-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111111111-1-11-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-1-1-1-1-11111111111111111-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-111111111-1-111-1-111-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11111-1-1-1-111-1-111-1-111
χ131111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-111-1-1-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1
χ17222222222-2-2222-2-22222-2-2-2-222-2-222-2-20000000022-2-2-200000000000000000000000000
χ18222222222-2-2222-2-22222-2-2-2-2-2-2-2-2-2-22200000000-2-222200000000000000000000000000
χ19222222222-2-2222-2-2-2-2-2-2222222-2-222-2-200000000-2-2-22200000000000000000000000000
χ20222222222-2-2222-2-2-2-2-2-22222-2-2-2-2-2-22200000000222-2-200000000000000000000000000
χ2122222222-222-2-2-2220000000022-2-2-2-2222222222200-200-2-20000-2-2000000000000000000
χ2222222222-222-2-2-2220000000022-2-2-2-222-2-2-2-2-2-2-2-200-20022000022000000000000000000
χ2322222222-222-2-2-22200000000-2-2-2-222-2-22222-2-2-2-200200-2-2000022000000000000000000
χ2422222222-222-2-2-22200000000-2-2-2-222-2-2-2-2-2-2222200200220000-2-2000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000200002i2i−2i−2i002i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000020000−2i−2i2i2i00−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-22222220000000000-200002i2i−2i−2i00−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-22222220000000000-20000−2i−2i2i2i002i2i−2i−2i00000000000000
χ29222-22-2-2-22222-2-2-2-222-2-222-2-2002-2000000000000000000000000000002-2002-200000000
χ30222-22-2-2-22222-2-2-2-222-2-222-2-2002-200000000000000000000000000000-2200-2200000000
χ31222-22-2-2-22222-2-2-2-2-2-222-2-222002-2000000000000000000000000000002-200-2200000000
χ32222-22-2-2-22222-2-2-2-2-2-222-2-222002-200000000000000000000000000000-22002-200000000
χ33222-22-2-2-22-2-22-2-22222-2-2-2-22200-2200000000000000000000000000000002i−2i00002i−2i0000
χ34222-22-2-2-22-2-22-2-22222-2-2-2-22200-220000000000000000000000000000000−2i2i0000−2i2i0000
χ35222-22-2-2-22-2-22-2-222-2-22222-2-200-2200000000000000000000000000000002i−2i0000−2i2i0000
χ36222-22-2-2-22-2-22-2-222-2-22222-2-200-220000000000000000000000000000000−2i2i00002i−2i0000
χ3722-2-2-22-22200-2-22002-22-200002i−2i002i−2i0022−2−2i2i2−i2−i22i−2i0002−22−22−2i2−i2i2−i2i2−i200000000000000
χ3822-2-2-22-22200-2-22002-22-200002i−2i002i−2i00−2−222−i2−i2i2i22i−2i000−22−22−22−i2i2−i2i2−i2i200000000000000
χ3922-2-2-22-22200-2-22002-22-20000−2i2i00−2i2i0022−2−2−i2−i2i2i2−2i2i0002−22−22−2−i2i2−i2i2−i2i200000000000000
χ4022-2-2-22-22200-2-22002-22-20000−2i2i00−2i2i00−2−222i2i2−i2−i2−2i2i000−22−22−22i2−i2i2−i2i2−i200000000000000
χ4122-2-2-22-22200-2-2200-22-2200002i−2i002i−2i0022−2−2i2i2−i2−i2−2i2i0002−2−22−22i2−i2−i2i2−i2i200000000000000
χ4222-2-2-22-22200-2-2200-22-2200002i−2i002i−2i00−2−222−i2−i2i2i2−2i2i000−222−22−2−i2i2i2−i2i2−i200000000000000
χ4322-2-2-22-22200-2-2200-22-220000−2i2i00−2i2i0022−2−2−i2−i2i2i22i−2i0002−2−22−22−i2i2i2−i2i2−i200000000000000
χ4422-2-2-22-22200-2-2200-22-220000−2i2i00−2i2i00−2−222i2i2−i2−i22i−2i000−222−22−2i2−i2−i2i2−i2i200000000000000
χ4522-2-2-22-22-20022-20000002i−2i2i−2i2i−2i00−2i2i0022−2−2i2i2−i2−i20002-2−22i2−i2−i2i2−i2i2−222−200000000000000
χ4622-2-2-22-22-20022-20000002i−2i2i−2i2i−2i00−2i2i00−2−222−i2−i2i2i20002-22−2−i2i2i2−i2i2−i22−2−2200000000000000
χ4722-2-2-22-22-20022-20000002i−2i2i−2i−2i2i002i−2i0022−2−2−i2−i2i2i2000-22−22i2−i2−i2i2i2−i22−2−2200000000000000
χ4822-2-2-22-22-20022-20000002i−2i2i−2i−2i2i002i−2i00−2−222i2i2−i2−i2000-222−2−i2i2i2−i2−i2i2−222−200000000000000
χ4922-2-2-22-22-20022-2000000−2i2i−2i2i2i−2i00−2i2i0022−2−2i2i2−i2−i2000-22−22−i2i2i2−i2−i2i22−2−2200000000000000
χ5022-2-2-22-22-20022-2000000−2i2i−2i2i2i−2i00−2i2i00−2−222−i2−i2i2i2000-222−2i2−i2−i2i2i2−i2−222−200000000000000
χ5122-2-2-22-22-20022-2000000−2i2i−2i2i−2i2i002i−2i0022−2−2−i2−i2i2i20002-2−22−i2i2i2−i2i2−i2−222−200000000000000
χ5222-2-2-22-22-20022-2000000−2i2i−2i2i−2i2i002i−2i00−2−222i2i2−i2−i20002-22−2i2−i2−i2i2−i2i22−2−2200000000000000
χ53444-44-4-4-4-444-444-4-40000000000-440000000000000000000000000000000000000000000
χ54444-44-4-4-4-4-4-4-4444400000000004-40000000000000000000000000000000000000000000
χ5544-44-4-44-4400-44-4004-4-44000000000000000000000000000000000000000000000000000
χ5644-44-4-44-4400-44-400-444-4000000000000000000000000000000000000000000000000000
χ5744-44-4-44-4-4004-440000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ5844-44-4-44-4-4004-44000000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ594-444-4-4-4404-40004-4000000000000000000000000000000000000000000000002i2−2i2000000
χ604-444-4-4-4404-40004-400000000000000000000000000000000000000000000000−2i22i2000000
χ614-444-4-4-440-44000-440000000000000000000000000000000000000000000000000002i2−2i200
χ624-444-4-4-440-44000-44000000000000000000000000000000000000000000000000000−2i22i200
χ634-44-4-444-404-4000-4400000000000000004i−4i4i−4i00000000000000000000000000000000000
χ644-44-4-444-404-4000-440000000000000000−4i4i−4i4i00000000000000000000000000000000000
χ654-44-4-444-40-440004-4000000000000000000004i−4i4i−4i0000000000000000000000000000000
χ664-44-4-444-40-440004-400000000000000000000−4i4i−4i4i0000000000000000000000000000000
χ674-4-4444-4-400000000000000000000004i−4i2i2−2i2−2i22i222−22−22220000000000000000000000000000000
χ684-4-4444-4-400000000000000000000004i−4i−2i22i22i2−2i2−222222−220000000000000000000000000000000
χ694-4-4444-4-40000000000000000000000−4i4i2i2−2i2−2i22i2−222222−220000000000000000000000000000000
χ704-4-4444-4-40000000000000000000000−4i4i−2i22i22i2−2i222−22−22220000000000000000000000000000000
χ718-8-8-88-888000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).